A similar relatedness between righteousness and teaching was made by Jesus when he admonished the disciples to a righteousness which exceeded that of the Pharisees. (Matthew 5:20) The context of the chapter concerns the commandments of God and keeping and teaching others to do so.
We are, that is, we have become, the walking embodiment of the righteousness, the teaching, of the will of God. This reality does not change or vary because of ourselves. Let us not diffuse or diminish the significance of these words with words of our own, "nobody is perfect." The notion of perfection as sinlessness is as foreign to the scriptures as is the doctrine of original sin. This reality of us as righteousness is in spite of ourselves and our fleshly tendencies. It is through the Holy Spirit who indwells us and it is what the saints of the faith that is in Christ Jesus are called to teach.